Wave Analysis Dashboard for the Irish Weather Buoy Network. All analysis computed via {targets} pipeline.

ImportantRogue Wave Definition

A rogue wave has Hmax/Hs > 2.0 (ratio of maximum individual wave to significant wave height).

Rows: 10,000
Columns: 22
$ time                 <dttm> 2019-01-01 00:00:00, 2019-01-01 02:00:00, 2019-0…
$ station_id           <chr> "M3", "M5", "M3", "M5", "M3", "M2", "M5", "M5", "…
$ call_sign            <chr> "62092", "62094", "62092", "62094", "62092", "620…
$ longitude            <dbl> -10.548261, -6.704336, -10.548261, -6.704336, -10…
$ latitude             <dbl> 51.21596, 51.69042, 51.21596, 51.69042, 51.21596,…
$ atmospheric_pressure <dbl> 1036.938, 1036.804, 1038.770, 1040.808, 1040.857,…
$ air_temperature      <dbl> 9.971, 11.045, 10.210, 12.461, 10.107, 7.627, 11.…
$ dew_point            <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, 9.3, NA, …
$ wind_direction       <dbl> 156, 278, 114, 33, 135, 109, 92, 103, 212, 238, 1…
$ wind_speed           <dbl> 3.415, 11.195, 10.389, 6.831, 11.385, 14.610, 11.…
$ gust                 <dbl> 5.835, 18.405, 13.804, 9.677, 15.227, 17.267, 13.…
$ relative_humidity    <dbl> 92.578, 72.266, 92.188, 88.281, 90.625, 66.797, 7…
$ sea_temperature      <dbl> 11.348, 10.928, 11.074, 10.986, 11.143, NA, 11.07…
$ salinity             <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ wave_height          <dbl> 2.500, 1.719, 2.344, 1.563, 2.188, NA, 1.250, 1.4…
$ wave_period          <dbl> 7.969, 6.797, 7.852, 7.969, 7.500, NA, 6.211, 5.0…
$ mean_wave_direction  <dbl> 255, 239, 243, 233, 284, NA, 236, 156, 139, NA, N…
$ hmax                 <dbl> 4.219, 2.578, 3.750, 2.109, 3.516, NA, 1.875, 1.6…
$ tp                   <dbl> 11.250, 12.070, 11.953, 11.719, 12.539, 3.750, 10…
$ thtp                 <dbl> 260.156, 237.656, 253.125, 229.219, 322.031, 59.0…
$ sprtp                <dbl> 29.531, 21.094, 33.750, 25.313, 39.375, 26.719, 1…
$ qc_flag              <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
Metric Value
Rogue Wave Events 1603
Stations Analyzed 5
Max Rogue Ratio 6.85
Max Hmax Observed 29.9 m
Dataset Start 2019-02-04 07:00 UTC
Dataset End 2026-02-05 13:00 UTC
Days in Dataset 2558
Analysis generated 2026-02-07 21:18 UTC using irishbuoys v0.1.0

Use the range slider at the bottom to zoom all panels to a specific time period.

rogue_ratio = Hmax/Hs (wave). Values > 2.0 define a rogue wave event. gust_ratio = Gust/Wind (wind). Values > 1.5 indicate a rogue gust.

ImportantRogue Gust Definition

A rogue gust has Gust/Wind > 1.5 (ratio of peak gust to sustained wind speed). This parallels the rogue wave definition (Hmax/Hs > 2.0).

Use the range slider at the bottom to zoom all panels to a specific time period.

gust_ratio = Gust/Wind. Values > 1.5 define a rogue gust event.

Comparing wave rogue events (Hmax/Hs > 2.0) with gust rogue events (Gust/Wind > 1.5).

Term Definition Reference
Hs = H1/3 = 4σ All three mean the same: significant wave height = mean of highest 1/3 of waves = 4 × standard deviation of sea surface Longuet-Higgins 1952
Hmax Maximum individual wave height in 17.5-min measurement period Typically Hmax/Hs ~ 1.5-1.9
Rogue Wave Wave where Hmax/Hs > 2.0 Dysthe 2008
Rogue Ratio = Hmax/Hs. Values > 2.0 indicate a rogue wave Used in Rogue Waves
Gust Ratio = Peak Gust / Sustained Wind. Typical value ~1.3 Used in Rogue Gusts
Rogue Gust Observation where Gust/Wind > 1.5 Used in Rogue Gusts
GEV Generalized Extreme Value distribution for annual maxima Used in Annual Max Model
GPD Generalized Pareto Distribution for peaks over threshold Used in Annual Max Prediction
Return Level Value expected to be exceeded once per T years Used in Annual Max Model

These three notations all mean the same thing:

  • Hs = Significant wave height (common abbreviation)
  • H1/3 = Mean of highest 1/3 of waves (original definition)
  • = 4 × standard deviation of sea surface elevation

The equivalence arises from the Rayleigh distribution of wave heights. For a narrow-banded wave spectrum, the theoretical relationship is Hs = 4 × sqrt(m0) where m0 is the variance of sea elevation.

  • Statistical requirement: Need ~100+ waves for valid H1/3
  • Wave periods typically 5-15 seconds → 17.5 min gives ~70-200 waves
  • WMO recommends 20-30 minutes; 17.5 is the practical lower bound
  • Trade-off: longer = better statistics, shorter = more temporal resolution

The Generalized Pareto Distribution (GPD) with Peaks Over Threshold (POT) approach fits extremes per station using all exceedances above a high threshold (90%, 95%, or 99% quantile).

Advantages over pooled GEV: - Uses many more data points (all exceedances, not just annual maxima) - Station-specific return levels - Multiple threshold sensitivity analysis

The Generalized Pareto Distribution has CDF for exceedances \(y = x - u\) above threshold \(u\):

\[F(y) = 1 - \left(1 + \frac{\xi y}{\sigma}\right)^{-1/\xi}\]

with two parameters:

Parameter Symbol Interpretation
Scale \(\sigma\) Spread of exceedances
Shape \(\xi\) Tail behaviour (same as GEV)

Return levels for T-year event:

\[z_T = u + \frac{\sigma}{\xi}\left[(n_y \lambda T)^\xi - 1\right]\]

where \(n_y\) = observations per year, \(\lambda\) = exceedance rate.

GPD results depend on threshold choice. Lower thresholds give more data but may violate asymptotic theory. The mev package provides diagnostics.

NoteLimited sample size (n=8 years)

The pooled GEV analysis below is illustrative only due to only 8 annual maxima. The GPD per-station approach (Tab 1) is preferred.

WarningExtensions for Production Use

Spatial dependence modelling: The SpatialExtremes package provides max-stable process models that account for joint extremes across stations.

Bayesian approaches: The mev package supports profile likelihood and Bayesian methods for improved uncertainty quantification.

Storm propagation: Cross-correlation lag analysis between stations could enable offshore-to-nearshore prediction with lead times.

Gust Factor = Peak Gust / Sustained Wind. Typical value ~1.3. Rogue Gust threshold: GF > 1.5 (see Rogue Gusts page for detailed analysis).

Term Definition Used In
Hs = H1/3 = 4σ Significant wave height = mean of highest 1/3 = 4×std dev Definitions
Hmax Max individual wave in 17.5-min period Rogue Waves
Rogue Wave Hmax/Hs > 2.0 Rogue Waves
Rogue Gust Gust/Wind > 1.5 Rogue Gusts
Gust Factor Peak Gust / Sustained Wind (~1.3 typical) Gust Factor
STL Seasonal-Trend decomposition (Loess) Trends
Method Description Used In
GEV Block maxima (annual max, n=8) Annual Max Model
GPD Peaks over threshold (all exceedances) Annual Max Prediction
Return Level Value exceeded once per T years Both EVA pages
Beaufort Description Wind Speed (m/s)
0-5 Calm to Fresh Breeze 0 - 10.7
6-7 Strong Breeze to Near Gale 10.8 - 17.1
8-9 Gale to Severe Gale 17.2 - 24.4
10 Storm 24.5 - 28.4
11 Violent Storm 28.5 - 32.6
12 Hurricane Force > 32.7
References:
  • Longuet-Higgins, M.S. (1952). Statistical distribution of sea waves. J. Marine Research, 11, 245-266.
  • Dysthe, K. et al. (2008). Oceanic rogue waves. Ann. Rev. Fluid Mech., 40, 287-310.
  • Coles, S. (2001). Statistical Modeling of Extreme Values. Springer.

Analysis generated 2026-02-07 21:18 UTC using irishbuoys v0.1.0